On the solutions of the operator equation XAX = BX
Hua Wang, Junjie Huang, Mengran Li · Linear and Multilinear Algebra · 2021
In this paper, some sufficient conditions and necessary conditions are established for existence of nonzero solutions of the operator equation XAX = BX on Hilbert spaces. Moreover, the necessary and sufficient condition which the solution of the equation is idempotent is also presented.